Algebra and Trigonometry

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Prerequisites

Modeling the Real World

Real Numbers

Integer Exponents

Rational Exponents and Radicals

Algebraic Expressions

Discovery Project: Visualizing a Formula

Factoring Algebraic Expressions

Rational Expressions

Chapter P Review

Chapter P Test

Focus on Problem Solving: General Principles

Equations and Inequalities

Basic Equations

Modeling with Linear Equations

Discovery Project: Equations Through the Ages

Quadratic Equations

Complex Numbers

Other Types of Equations

Inequalities

Absolute Value Equations and Inequalities

Chapter 1 Review

Chapter 1 Test

Focus on Modeling: Making the Best Decisions

Coordinates and Graphs

The Coordinate Plane

Discovery Project: Visualizing Data

Graphs of Equations in Two Variables

Graphing Calculators: Solving Equations and Inequalities Graphically

Lines

Modeling: Variation

Chapter 2 Review

Chapter 2 Test

Focus on Modeling: Fitting Lines to Data

Functions

What is a Function? Graphs of Functions

Discovery Project: Relations and Functions

Increasing and Decreasing Functions: Average Rate of Change

Transformations of Functions

Quadratic Functions: Maxima and Minima

Combining Functions

Discovery Project: Iteration and Chaos

One-to-One Functions and Their Inverses

Chapter 3 Review

Chapter 3 Test

Focus on Modeling: Modeling With Functions

Polynomial And Rational Functions

Polynomial Functions and Their Graphs

Dividing Polynomials

Real Zeros of Polynomials

Discovery Project: Zeroing in on a Zero

Complex Zeros and the Fundamental Theorem of Algebra

Rational Functions

Chapter 4 Review

Chapter 4 Test

Focus on Modeling: Fitting Polynomial Curves to Data

Exponential and Logarithmic Functions

Exponential Functions

Discovery Project: Exponential Explosion

Logarithmic Functions

Laws of Logarithms

Exponential and Logarithmic Equations

Modeling with Exponential and Logarithmic Functions

Chapter 5 Review

Chapter 5 Test

Focus on Modeling: Fitting Exponential and Power Curves to Data

Trigonometric Functions of Angles

Angle Measure

Trigonometry of Right Triangles

Trigonometric Functions of Angles

Discovery Project: Similarity

The Law of Sines

The Law of Cosines

Chapter 6 Review

Chapter 6 Test

Focus on Modeling: Surveying

Trigonometric Functions of Real Numbers

The Unit Circle

Trigonometric Functions of Real Numbers

Trigonometric Graphs

Discovery Project: Predator-Prey Models

More Trigonometric Graphs

Modeling Harmonic Motion

Chapter 7 Review

Chapter 7 Test

Focus on Modeling: Fitting Sinusoidal Curves to Data

Analytic Trigonometry

Trigonometric Identities

Addition and Subtraction Formulas

Double-Angle, Half-Angle, and Sum-Product Identities

Inverse Trigonometric Functions

Discovery Project:Where to Sit at the Movies

Trigonometric Equations

Chapter 8 Review

Chapter 8 Test

Focus on Modeling: Traveling and Standing Waves

Polar Coordinates and Vectors

Polar Coordinates

Graphs of Polar Equations

Polar Form of Complex Numbers

DeMoivre's Theorem

Discovery Project: Fractals

Vectors

The Dot Product

Discovery Project: Sailing Against the Wind

Chapter 9 Review

Chapter 9 Test

Focus on Modeling: Mapping the World

Systems Of Equations and Inequalities

Systems of Equations

Systems of Linear Equations in Two Variables

Systems of Linear Equations in Several Variables

Discovery Project: Best Fit versus Exact Fit

Systems of Linear Equations: Matrices

The Algebra of Matrices

Discovery Project: Will the Species Survive? Inverses of Matrices and Matrix Equations